Applied Probability
نویسندگان
چکیده
1 Basic aspects of continuous time Markov chains 3 1.1 Markov property . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.2 Regular jump chain . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 1.3 Holding times . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 1.4 Poisson process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 1.5 Birth process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 1.6 Construction of continuous time Markov chains . . . . . . . . . . . . . . . . . . . . . 12 1.7 Kolmogorov’s forward and backward equations . . . . . . . . . . . . . . . . . . . . . 15 1.7.1 Countable state space . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 1.7.2 Finite state space . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 1.8 Non-minimal chains . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
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